Spreading of pathological proteins through brain networks: A case study for Alzheimer's disease

Germana Landi; Arianna Scaravelli; Maria Carla Tesi; Claudia Testa; Germana Landi; Arianna Scaravelli; Maria Carla Tesi; Claudia Testa

doi:10.3934/mbe.2026024

Mathematical Biosciences and Engineering

2026, Volume 23, Issue 3: 619-635. doi: 10.3934/mbe.2026024

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Spreading of pathological proteins through brain networks: A case study for Alzheimer's disease

1.
Department of Mathematics, University of Bologna, Italy
2.
Department of Physics and Astronomy "Augusto Righi'', University of Bologna, Italy

Received: 22 October 2025 Revised: 16 December 2025 Accepted: 24 December 2025 Published: 27 January 2026

Given the complexity, unknown causes, and lack of effective treatments for Alzheimer's disease (AD), mathematical modeling offers a valuable approach to its understanding. Models, once validated, offer a powerful tool to test medical hypotheses that are otherwise difficult to directly verify. Here, our focus is to elucidate the spread of misfolded $ \tau $ protein, a critical hallmark of AD alongside A$ \beta $ protein, while taking the synergistic interaction between the two proteins into account. We consider distinct modeling choices, all employing network frameworks for protein evolution, differentiated by their network architecture and diffusion operators. By carefully comparing these models against clinical $ \tau $ concentration data, gathered through advanced multimodal analysis techniques, we show that certain models replicate better the protein's dynamics. This investigation underscores a crucial insight: when modeling complex pathologies, the precision with which the mathematical framework is chosen is crucial, especially when validation against clinical data is considered decisive.
- Alzheimer's disease,
- mathematical models on graphs,
- $ A\beta $ and $ \tau $ proteins,
- medical imaging,
- numerical simulations
Citation: Germana Landi, Arianna Scaravelli, Maria Carla Tesi, Claudia Testa. Spreading of pathological proteins through brain networks: A case study for Alzheimer's disease[J]. Mathematical Biosciences and Engineering, 2026, 23(3): 619-635. doi: 10.3934/mbe.2026024

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Abstract

Given the complexity, unknown causes, and lack of effective treatments for Alzheimer's disease (AD), mathematical modeling offers a valuable approach to its understanding. Models, once validated, offer a powerful tool to test medical hypotheses that are otherwise difficult to directly verify. Here, our focus is to elucidate the spread of misfolded $ \tau $ protein, a critical hallmark of AD alongside A$ \beta $ protein, while taking the synergistic interaction between the two proteins into account. We consider distinct modeling choices, all employing network frameworks for protein evolution, differentiated by their network architecture and diffusion operators. By carefully comparing these models against clinical $ \tau $ concentration data, gathered through advanced multimodal analysis techniques, we show that certain models replicate better the protein's dynamics. This investigation underscores a crucial insight: when modeling complex pathologies, the precision with which the mathematical framework is chosen is crucial, especially when validation against clinical data is considered decisive.

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